Factor of Safety for Tri-axial State of Stress Calculator

↳

⤿

Design of Coupling

Basics Of Machine Design

Design of Gears

⤿

Design of Bushed-Pin Flexible Coupling

Design of Clamp and Muff Coupling

Design of Cotter Joint

Design of Knuckle Joint

Design of Rigid Flange Coupling

Design of Threaded Fastener

Packing

Retaining Rings and Circlips

Riveted Joints

Seals

Threaded Bolted Joints

Welded Joints

✖Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions.ⓘ Tensile Yield Strength [σ_yt]			+10% -10%
✖A normal stress 1 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 1 [σ₁]			+10% -10%
✖A normal stress 2 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 2 [σ₂]			+10% -10%
✖Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 3 [σ₃]			+10% -10%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety for Tri-axial State of Stress [f_s]

⎘ Copy

👎

Formula

✖

Factor of Safety for Tri-axial State of Stress

Formula

`"f"_{"s"} = "σ"_{"yt"}/sqrt(1/2*(("σ"_{"1"}-"σ"_{"2"})^2+("σ"_{"2"}-"σ"_{"3"})^2+("σ"_{"3"}-"σ"_{"1"})^2))`

Example

`"0.207058"="8.5N/m²"/sqrt(1/2*(("87.5"-"51.43N/m²")^2+("51.43N/m²"-"96.1N/m²")^2+("96.1N/m²"-"87.5")^2))`

Calculator

LaTeX

Reset

👍

Download Design of Coupling Formula PDF

Factor of Safety for Tri-axial State of Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))
f_s = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Tensile Yield Strength - (Measured in Pascal) - Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions.
Normal Stress 1 - A normal stress 1 is a stress that occurs when a member is loaded by an axial force.
Normal Stress 2 - (Measured in Pascal) - A normal stress 2 is a stress that occurs when a member is loaded by an axial force.
Normal Stress 3 - (Measured in Pascal) - Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.

STEP 1: Convert Input(s) to Base Unit

Tensile Yield Strength: 8.5 Newton per Square Meter --> 8.5 Pascal (Check conversion here)
Normal Stress 1: 87.5 --> No Conversion Required
Normal Stress 2: 51.43 Newton per Square Meter --> 51.43 Pascal (Check conversion here)
Normal Stress 3: 96.1 Newton per Square Meter --> 96.1 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) --> 8.5/sqrt(1/2*((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2))

Evaluating ... ...

f_s = 0.207058141408265

STEP 3: Convert Result to Output's Unit

0.207058141408265 --> No Conversion Required

FINAL ANSWER

0.207058141408265 ≈ 0.207058 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Design of Machine Elements » Design of Coupling » Factor of Safety for Tri-axial State of Stress

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 9 Design of Coupling Calculators

Factor of Safety for Tri-axial State of Stress

Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

Equivalent Stress by Distortion Energy Theory

Go Equivalent Stress = 1/sqrt(2)*sqrt((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)

Factor of Safety for Bi-Axial State of Stress

Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Tensile Stress in Spigot

Go Tensile Stress = Tensile Force on Rods/((pi/4*Diameter of Spigot^(2))-(Diameter of Spigot*Thickness of Cotter))

Polar Moment of Inertia of Hollow Circular Shaft

Go Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32

Permissible Shear Stress for Cotter

Go Permissible Shear Stress = Tensile Force on Rods/(2*Mean Width of Cotter*Thickness of Cotter)

Permissible Shear Stress for Spigot

Go Permissible Shear Stress = Tensile Force on Rods/(2*Spigot Distance*Diameter of Spigot)

Stress Amplitude

Go Stress Amplitude = (Maximum Stress at Crack Tip-Minimum Stress)/2

Polar Moment of Inertia of Solid Circular Shaft

Go Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32

< 17 Maximum Shear Stress and Principal Stress Theory Calculators

Factor of Safety for Tri-axial State of Stress

Go Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2))

Diameter of Shaft given Permissible Value of Maximum Principle Stress

Go Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3)

Permissible Value of Maximum Principle Stress

Go Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2))

Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory

Go Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3)

Bending Moment given Maximum Shear Stress

Go Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)

Torsional Moment given Maximum Shear Stress

Go Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2)

Maximum Shear Stress in Shafts

Go Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety for Bi-Axial State of Stress

Go Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Torsional Moment given Equivalent Bending Moment

Go Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)

Equivalent Bending Moment given Torsional Moment

Go Equivalent Bending Moment from MSST = Bending Moment in Shaft for MSST+sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)

Factor of Safety given Permissible Value of Maximum Shear Stress

Go Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST

Yield Strength in Shear Maximum Shear Stress Theory

Go Shear Yield Strength in Shaft from MSST = 0.5*Factor of Safety of Shaft*Maximum Principle Stress in Shaft

Permissible Value of Maximum Shear Stress

Go Maximum Shear Stress in Shaft from MSST = 0.5*Yield Strength in Shaft from MSST/Factor of Safety of Shaft

Yield Stress in Shear given Permissible Value of Maximum Principle Stress

Go Yield Strength in Shaft from MPST = Maximum Principle Stress in Shaft*Factor of Safety of Shaft

Permissible Value of Maximum Principle Stress using Factor of Safety

Go Maximum Principle Stress in Shaft = Yield Strength in Shaft from MPST/Factor of Safety of Shaft

Factor of Safety given Permissible Value of Maximum Principle Stress

Go Factor of Safety of Shaft = Yield Strength in Shaft from MPST/Maximum Principle Stress in Shaft

Factor of Safety given Ultimate Stress and Working Stress

Go Factor of Safety = Fracture Stress/Working Stress

Factor of Safety for Tri-axial State of Stress Formula

Define Factor of Safety?

The factor of safety (FoS) is the ability of a system's structural capacity to be viable beyond its expected or actual loads. An FoS may be expressed as a ratio that compares absolute strength to the actual applied load, or it may be expressed as a constant value that a structure must meet or exceed according to law, specification, contract or standard.

How to Calculate Factor of Safety for Tri-axial State of Stress?

Factor of Safety for Tri-axial State of Stress calculator uses Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)) to calculate the Factor of Safety, The Factor of Safety for Tri-axial State of Stress is the ability of a system's structural capacity to be viable beyond its expected or actual loads. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety for Tri-axial State of Stress using this online calculator? To use this online calculator for Factor of Safety for Tri-axial State of Stress, enter Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃) and hit the calculate button. Here is how the Factor of Safety for Tri-axial State of Stress calculation can be explained with given input values -> 0.207058 = 8.5/sqrt(1/2*((87.5-51.43)^2+(51.43-96.1)^2+(96.1-87.5)^2)).

FAQ

What is Factor of Safety for Tri-axial State of Stress?

The Factor of Safety for Tri-axial State of Stress is the ability of a system's structural capacity to be viable beyond its expected or actual loads and is represented as f_s = σ_yt/sqrt(1/2*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)) or Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)). Tensile Yield Strength is the stress a material can withstand without permanent deformation or a point at which it will no longer return to its original dimensions, A normal stress 1 is a stress that occurs when a member is loaded by an axial force, A normal stress 2 is a stress that occurs when a member is loaded by an axial force & Normal Stress 3 is a stress that occurs when a member is loaded by an axial force.

How to calculate Factor of Safety for Tri-axial State of Stress?

The Factor of Safety for Tri-axial State of Stress is the ability of a system's structural capacity to be viable beyond its expected or actual loads is calculated using Factor of Safety = Tensile Yield Strength/sqrt(1/2*((Normal Stress 1-Normal Stress 2)^2+(Normal Stress 2-Normal Stress 3)^2+(Normal Stress 3-Normal Stress 1)^2)). To calculate Factor of Safety for Tri-axial State of Stress, you need Tensile Yield Strength (σ_yt), Normal Stress 1 (σ₁), Normal Stress 2 (σ₂) & Normal Stress 3 (σ₃). With our tool, you need to enter the respective value for Tensile Yield Strength, Normal Stress 1, Normal Stress 2 & Normal Stress 3 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Factor of Safety?

In this formula, Factor of Safety uses Tensile Yield Strength, Normal Stress 1, Normal Stress 2 & Normal Stress 3. We can use 2 other way(s) to calculate the same, which is/are as follows -

Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))
Factor of Safety = Tensile Yield Strength/(sqrt(Normal Stress 1^2+Normal Stress 2^2-Normal Stress 1*Normal Stress 2))

Home

FREE PDFs

🔍 Search